A shopkeeper sells three types of flower seeds \(A_1\), \(A_2\), \(A_3\). They are sold as a mixture where the proportions are 4 : 4 : 2 respectively. The germination rates of the three types of seeds are 45%, 60% and 35% respectively. Calculate the probability in the following cases.
The probability of a randomly chosen seed to germinate is :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(\displaystyle\frac{49}{100}\)
Let G be the event that the seed germinates. The proportions 4 : 4 : 2 give
\(P(A_1) = 0.4,\quad P(A_2) = 0.4,\quad P(A_3) = 0.2\)
and the germination rates give
\(P(G \mid A_1) = 0.45,\quad P(G \mid A_2) = 0.60,\quad P(G \mid A_3) = 0.35\)
By the theorem of total probability:
\(P(G) = 0.4 \times 0.45 + 0.4 \times 0.60 + 0.2 \times 0.35\)
\(= 0.18 + 0.24 + 0.07 = 0.49\)
\( \displaystyle = \frac{49}{100} \)
NCERT Exemplar:
Probability
